Question

углы при одном из оснований трапеции равны 44 и 46 (градусов) ,а отрезки, соединяющие середины противоположных сторон трапеции равны 6 см и 14 см. найдите основания трапеции

Answer 1

Трапеция АВСД, уголА=44, уголД=46, ЛЕ-средняя линия=14, МТ=6, Н-точка пересечения ЛЕ и МТ, продлеваем боковые стороны до пересечения в точке К, треугольник АКД прямоугольный, угол К=180-уголА-уголД=180-44-46=90,  ЛЕ делит МТ на две равные части МН=НТ=МТ/2=6/2=3, МТ делит ЛЕ на две равные части ЛН=НЕ=ЛЕ/2=14/2=7, треугольник ЛКЕ прямоугольный ЛЕ гипотенуза, КН - медиана в прямоугольном треугольнике=1/2 гипотенузыЛЕ=14/2=7, КМ=КН-МН=7-3=4, КМ-медиана в прямоугольном треугольнике ВКС=1/2 гипотенузыВС, ВС=2*КМ=2*4=8, ЛЕ=(ВС+АД)/2, АД=2ЛЕ-ВС=2*14-8=20

Answer 2

Finding the Bases of the Trapezoid

To find the bases of the trapezoid, we can use the information given about the angles and the lengths of the segments connecting the midpoints of the opposite sides.

Let's denote the bases of the trapezoid as b1 and b2.

Given: - The angles at one of the bases are 44 degrees and 46 degrees. - The lengths of the segments connecting the midpoints of the opposite sides are 6 cm and 14 cm.

To find the bases, we can use the fact that the angles at the bases of a trapezoid are supplementary (add up to 180 degrees).

Let's solve for b1 and b2 using the given information:

1. We know that the sum of the angles at one of the bases is 44 degrees + 46 degrees = 90 degrees. 2. Since the angles at the bases are supplementary, the sum of the angles at the other base is also 90 degrees. 3. Let's assume that the angles at the other base are x degrees and (90 - x) degrees. 4. Using the fact that the angles at the bases of a trapezoid add up to 180 degrees, we can write the equation: x + (90 - x) = 180. 5. Solving the equation, we find that x = 90 degrees. 6. Therefore, the angles at the other base are 90 degrees and 0 degrees.

Now, let's consider the lengths of the segments connecting the midpoints of the opposite sides.

1. The lengths of the segments connecting the midpoints of the opposite sides are 6 cm and 14 cm. 2. These segments are parallel to the bases of the trapezoid. 3. Since the segments connecting the midpoints of the opposite sides are parallel to the bases, they are also congruent. 4. Therefore, the lengths of the bases are 6 cm and 14 cm.

In conclusion, the bases of the trapezoid are 6 cm and 14 cm.

Please let me know if you need any further assistance!